OFFSET
1,3
COMMENTS
Equivalent to 0^2 + 1^2 + 2^2 + 3^2 + ... + r^2 = 0 + 1 + 2 + 3 + ... + s = n for some r and s.
REFERENCES
Joe Roberts, Lure of the Integers, page 245 (entry for 645).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, p. 108.
LINKS
R. Finkelstein and H. London, On triangular numbers which are sums of consecutive squares, J. Number Theory 4 (1972), 455-462.
M. Gardner, Letter to N. J. A. Sloane, circa Aug 11 1980, concerning A001110, A027568, A039596, etc.
H. E. Thomas Jr., Problem 5634, Amer. Math. Monthly, 75 (1968), p. 1018.
EXAMPLE
1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 2 + 3 + ... + 10 = 55, so 55 is in the sequence.
MAPLE
q:= n-> issqr(8*n+1):
select(q, [sum(j^2, j=1..n)$n=0..100])[]; # Alois P. Heinz, Oct 17 2024
CROSSREFS
KEYWORD
fini,nonn,full
AUTHOR
EXTENSIONS
Additional comments from Jud McCranie, Mar 19 2000
Zero inserted by Daniel Mondot, Sep 07 2023
STATUS
approved